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Section 3.4
Equations of a Line
Recall from the previous section, if given the equation of a line,
we may find the slope of the line as follows:
1)
2)
Example 1
Given the following equation of a line,
(a) Solve for .
(b) What is the slope of the line?
(c) Find the -intercept of the line.
Slope-Intercept Form of the Equation of a Line
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Example 2
Identify the slope and -intercept of each line.
(a)
Slope: _________
-int: _________
(b)
Slope: _________
-int: _________
(c)
Slope: _________
-int: _________
(d)
Slope: _________
-int: _________
Example 3
Find an equation of the line with slope
and -intercept
.
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Example 4
Graph the line with -intercept
and slope
.
Example 5
Graph the line passing through the
point
with slope
.
Example 6
Graph the line passing through
the point
with
.
Example 7
Graph the line passing through the
point
with undefined slope.
Example 8
Graph the equation of the line by using the slope and -intercept.
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Example 9
Write an equation in slope-intercept form of the line passing through the point
slope
.
with
In this last example, we were given a point on the line, and the slope of the line.
Since we didn’t know the -intercept, we could not immediately write the equation of the line
in slope-intercept form. We had to do a little bit of work to first find the -intercept.
Wouldn’t it be nice if there was a form of the equation of a line that didn’t
require that we know the -intercept?
Let’s derive another form of the equation of a line!
Suppose you are given that the point
is on a line with slope
.
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Point-Slope Form of the Equation of a Line
Example 10
Write an equation for the line passing through the point
Give the final answer in slope-intercept form.
Example 11
Write an equation for the line passing through the point
with slope
.
with undefined slope.
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Example 12
Write an equation for the line passing through the points
Give the final answer in slope-intercept form.
and
.
Example 13
Write an equation for the line passing through the points
and
.
Example 14
Write an equation of the line passing through the point
and perpendicular to
.